Discretization of the Density Matrix as a Nonlinear Positive Map and Entanglement


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Abstract

We propose the discretization of the density matrix as a nonlinear positive map for systems with continuous variables. We use this procedure for calculating the entanglement between two modes through different criteria, such as Tsallis entropy, von Neumann entropy and linear entropy, and the logarithmic negativity. As an example, we study the dynamics of entanglement for the two-mode squeezed-vacuum state in the parametric amplifier and show good agreement with the analytic results. Also we address the loss of information on the system state due to the discretization of the density matrix.

About the authors

Julio A. López-Saldívar

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México

Author for correspondence.
Email: julio.lopez@nucleares.unam.mx
Mexico, Apdo. Postal 70-543, México, D.F., 04510

Armando Figueroa

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México

Email: julio.lopez@nucleares.unam.mx
Mexico, Apdo. Postal 70-543, México, D.F., 04510

Octavio Castaños

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México

Email: julio.lopez@nucleares.unam.mx
Mexico, Apdo. Postal 70-543, México, D.F., 04510

Ramón López–Peña

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México

Email: julio.lopez@nucleares.unam.mx
Mexico, Apdo. Postal 70-543, México, D.F., 04510

Margarita A. Man’ko

Lebedev Physical Institute, Russian Academy of Sciences

Email: julio.lopez@nucleares.unam.mx
Russian Federation, Leninskii Prospect 53, Moscow, 119991

Vladimir I. Man’ko

Lebedev Physical Institute, Russian Academy of Sciences; Moscow Institute of Physics and Technology (State University)

Email: julio.lopez@nucleares.unam.mx
Russian Federation, Leninskii Prospect 53, Moscow, 119991; Dolgoprudnyi, Moscow Region, 141700

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